In this paper, the frequency splitting phenomenon is precisely investigated based on the concept of the maximum power transfer theorem for a two-coil wireless power transfer (WPT) system. Here, unlike the previous studies, in which the analysis were performed by the reflected impedance, the scrutiny is conducted based on the thevenin equivalent impedance. First, the cause of the frequency splitting phenomenon is described using the frequency characteristics of the thevenin impedance and the load power. Second, the splitting equation is derived and the splitting frequencies are calculated through it. Eventually, some methods, that have been used so far to improve the power transfer capability, in the presence of the frequency splitting phenomenon, are mentioned. In addition, using simulation results by MATLAB software, these methods are compared together and the best method is obtained.